Three parallel plate capacitors $$C_1$$, $$C_2$$ and $$C_3$$ each of capacitance 5 $$\mu$$F are connected as shown in figure. The effective capacitance between points A and B, when the space between the parallel plates of $$C_1$$ capacitor is filled with a dielectric medium having dielectric constant of 4, is :

Initially

$$C_1=C_2=C_3=5\mu F$$

Dielectric constant 4 is inserted in $$C_1$$​, so

$$C_1'=4(5)=20\mu F$$

From circuit:

• Top branch: $$C_1\ ​and\ C_2$$ are in series
• Bottom branch:$$C_3$$ alone

These two branches are in parallel.

Top branch equivalent

$$C_{top}=\frac{C_1'C_2}{C_1'+C_2}$$

$$=\frac{20\cdot5}{20+5}$$

$$\frac{100}{25}=4\mu F$$

Total equivalent

Parallel combination:

$$C_{eq}=C_{top}+C_3$$

$$=4+5$$

$$=9\mu F$$